The impact of subgrid-scale motions on a background flow, including the molecular motion and small turbulent eddies, is referred to as the frictional effect. The atmosphere is a weakly viscous fluid, but friction is important wherever the velocity gradient is very large. The frictional effect is therefore strong at least in a layer next to the surface of the Earth. Such a layer is called the boundary layer elaborated in Section 4.2. The representation of the subgrid-scale influence of small turbulent eddies on a background flow is elaborated in Section 4.3. A simple representation of small turbulence eddies is given in Section 4.5. We define and examine the dynamics of several types of boundary layers in Sections 4.6, 4.9 and 4.10. The dynamics of the atmospheric Ekman layer and the oceanic Ekman layer is particularly important for large-scale geophysical flows and is elaborated in Sections 4.7 and 4.8. Although the frictional effect is generally unimportant in the short-term evolution of a geophysical flow, it would exert a strong influence on the long-term evolution through its coupling with the boundary layer.

Scale and estimate of the frictional force

The frictional force in large-scale disturbances at a level one-kilometer or more above the surface is weak compared to other forces. That is evident in the fact that wind at those levels is approximately in geostrophic balance. Nevertheless, the frictional force becomes progressively stronger at lower and lower levels.